How have I lived this long and not known such key facts for life under (((usurers)))? Though it makes perfect sense I would never have guessed that the usurers would "send good money after bad," but I can see that they would not want to lose even a single [imaginary] decimal point.
No, they don't want to lose the security behind the mortgage (i.e., the home and land) to a tax lien that takes precedence over all other liens, but neither do they want to foreclose --- neither the corporate lenders, nor the government-chartered lenders such as FNMA and Freddie Mac, want to come into possession of homes. Then they just have to turn around and sell them. Nobody wins in a foreclosure. Typically they will "work with someone" from six months to a year and even longer, and some delinquent borrowers know this, and work it to their own advantage. Foreclosure is truly a last resort.
Yes, in theory, strict letter of the contract, the entire amount becomes due and payable one day after a payment is missed, but in actual practice, it drags out for a long time, during which time, many borrowers will send a little bit of what is due, or one month's payment where two are due, and so on, under the rubric of "it's not as though we're not paying at all, we're paying what we can". Sometimes they will call and ask if they can skip a payment and put it "on the back", i.e., extend the payment term. Can't do that either. Again, lenders bend over backwards, and put up with every form of shenanigans you can imagine (I've seen it all!), to prevent a foreclosure. Again, it's a last resort.